Order of reaction

The sum of the exponents of the concentration terms in the rate expression is known as the order of reaction.

For homogeneous reaction,

mA + nB = Product

Rate of reaction,   

Overall order of entire reaction = (m + n)

Order of reaction with respect to A = m

Order of reaction with respect to B = n

For the rate expression of 

 

 

Reaction is zero order if n = 0

Reaction is 1st order if n = 1

Reaction is 2nd order if n = 2

Zero order reaction:

A reaction is of zero order when the rate of reaction is independent of the concentration of materials. The rate of reaction is a constant. When the limiting reactant is completely consumed, the reaction stops abruptly.
  The zero order rate law for the general reaction 

  

 Let Ao = Initial or original color concentration at time to

At = Final concentration by fading at time t

 

 

If, Ao   = c and after time t the amount of reactant reacted is x then,

At = c – x

Putting this values in no 1 equation,

C –x = c - kot

X = kot………………………………………………………….2

 

Half life of zero order reaction:

Half life is defined as the time required for concentration of a reactant to decrease to half of its initial value;

When; 

 

  

From zero order rate expression,

 

First order reaction:

   

In first order reaction, the rate of reaction is proportional to the concentration of one of the reactants.

 When in rate expression,

 

  It is called first order reaction.

Rate expression:

For first order reaction

A→ product.

Where the equilibrium conc. Of A is c,

Then,

 

 

 

The value of  k:

 

 

Half life of first order reaction:

 

 

Second order reaction:

The rate of a second order reaction is proportional to either the concentration of a reactant squared, or the product of concentrations of two reactants.

For the general case of a reaction between A and B, such that



the rate of reaction will be given by

 

 

A plot of  1 / [A]   vs   t   produces a straight line with slope   k and intercept   1 / [A]₀  . The plot should be linear up to a conversion of about 50%.

2. Starting concentrations of the two reactants are different:

If [A]₀ and [B]₀ are different the variable x is used. 

Equation (1) becomes 

 

     

where [A]₀ - x = [A], [B]₀ - x = [B] and x is the decrease in the concentration of A and B. 

Equation  (5) can be integrated after separation of the variables and partial fraction expansion. The result is:

 

where C is the constant of integration. 

Using the condition that x = 0, when t = 0, the value of C can be found

 

 against t will have a positive slope, equal ([A]₀ - [B]₀) k. 

  If the experimental method yields reactant concentrations rather than x, the equivalent form of equation (8)  is; 

 

Because equivalent amounts of A and B are reacting, [A] can be expressed in terms of [B].

If [B] = x , [A] = [A]₀ - (x₀ - x)

Provided that the initial concentration of A is twice the initial concentration of B

 

 

References:


1. Physical Chemistry
    (Peter Atkins, Julio De Paula)
2. Wikipedia
3. A Textbook of Physical Chemistry
    (K K Sharma)
4. Physical Chemistry
    (Thomas Engel)